Is it possible to make a cut from ortho view through the whole object that is measured 1cm from this edge?
While the answer from @Robin-Betts is working in many cases, there are those situations where the cut would go through different loops and thus a loop cut with later adjustment would not work.

Here a solution that should work no matter what:


Select a vertex that lies along an edge from where you want the precise distance.
Duplicate the vertex with Shift+D and press Z to make sure it stays on that axis. Move the vertex above the object.
Press G followed by Y in this case to restrict the movement again and then enter the distance you desire the cut to be made at.(I used a specific distance to showcase the mentioned situation with a possible cut over multiple loops.)
Extrude with E from the vertex once to the left and once to the top and create a face (you can restrict the extrusion with Y and Z, but it's not absolutely needed here, as only the first duplicated vertex is needed to be precisely where it is). A triangle face is fine, as it's just a workaround to get an anchor for the knife tool. For some reason a single vertex as well as an edge won't let you snap to it with the knife tool.
Now you can activate the knife tool with K and it will find the vertex we first duplicated to use as startpoint.
Activate the angle constraint with C and cut through 
with Z and pull the cut under the object to have the cut encompass the entire object.
Accept with LMB and confirm the cut with Enter


You can now delete the knife anchor face.

Here a more visual explanation: